Path-dependent measures of risks: drawdowns, occupation times and Parisian times

点击翻译按钮获取中文摘要

As in the 2007-2008 financial crisis, we have experienced a complete cycle of booms and busts: the economic bubble before the crisis, the sudden crash of the market, as well as the recession thereafter. The financial crisis not only caused huge damage to the global economy but also had extensive impact on the practice of quantitative risk management in insurance and finance. It prompts researchers in Canada and all over the world to develop and improve mathematical models to better characterize and measure these extreme risks. The proposed research will systematically study drawdowns, occupation times, and Parisian times (DOP) which serve as natural models to characterize and measure the extreme risks of crash and depression. Because of the features of path dependency, DOP are able to provide with more reliable and comprehensive information on the performance of insurance businesses or investment portfolios in a time period. Then, risk management decisions can be taken in a timely manner which is of paramount importance. Moreover, much of recent research has showed that DOP have wide applications in modeling various events, instruments and regulations in insurance and finance.The objectives of this proposed research are (1) to develop fundamental theory and general methodology in both theoretical analysis and numerical computation of DOP; (2) to pursue a better understanding of extreme risks such as crash and depression; (3) to improve quantitative risk management techniques to measure and reduce the extreme risks. The proposed research will produce 2-3 sole or joint papers per year to be published in the top tier journals in actuarial science, applied probability or mathematical finance. Graduate students and exceptional undergraduate students will be intensively involved in this proposed research program.